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A two-dimensional electrostatic field varies with the coordinates x and y, but is independent of z. Show that the average value of the potential V on any circle in the x-y plane is equal to the value of the potential at the center of the circle provided that there is no charge inside the circle. [Hint: Consider a circle of uniform charge per unit length lambda=Q/(2*pi*a). Find V at a point outside the circle in two ways: using Gauss' law, and by direct integration. Do not carry out this last integral; just set it up. Now look at the equality between the integral and the result of Gauss' law, and interpret what it is saying.
Starting from rest, a disk rotates about its central axis withconstant angular acceleration. In 8.0s, it rotates 10 rad. What was the angular acceleration during this time
Constable Bob inspected skid marks near a traffic accident to determine the acceleration of initial velocity of lawn mower involved in the accident. Bob measured the lawn mower skid marks to be 32 m long. Witnesses said the lawn mower was skiddin..
Galaxies form by gravitational collapse of regions that are denser than average. Noting that the present day average mass density of the universe is ρ = 3 × 10-30 g/cm-3, estimate how long it takes for a galaxy to collapse.
A light bulb is connected to a 120.0-V wall socket. The current in the bulb depends on the time t according to the relation I = (0.884 A) sin [(333 Hz)t]. What is the average power delivered to the light bulb
A 38.0 kg child swings in a swing supported by two chains, each 3.04m long. The tension in each chain at the lowest point is 429N. Find out the child's speeds at the lowest point.
A 44.5 mA current is carried by a uniformly wound air-core solenoid with 435 turns, a 20.0 mm diameter, and 14.5 cm length. Compute the magnetic flux through each turn
In the H atom the radius of orbit B is 16 times greater than the radius of orbit A. What is the total energy of the electron in orbit B
A lawn mower in the form of a thin-walled, hollow cylinder withmass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle, find the acceleration and friction force
A person with a mass of 95 kg and a volume of 0.101 m3 floats quietly in water. What is the volume of the person that is above water
Two point particles with masses m and 4m are placed along the x-axis at x = - a, Calculate the gravitational field and gravitational potential at x = 0
A person lifts a 5kg cement block a vertical distance of 2.3m and after that aeries the block horizontally a distance of 6m. Determine the work completed by the person and by the force of gravity in this process.
a rock band playing an outdoor concert produces sound at120 rm db 5.0 rm m away from their single working loudspeaker.
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